133 Responses

General response: Thanks to everyone for their comments (even the depressingly snarky ones) on my paper. I'll now try to respond individually to people's points. It'll probably take me at least 30 minutes to get all the separate replies posted...

The key feminist who's sought extensive, direct state support for arbitrary caretaker-dependant units, and argued that civil marriage has distracted the state from (and has been an inaccurate and prejudicial proxy for the state) directly tracking and supporting the diverse forms that care-delivery takes in society is Martha Fineman. She concludes that civil marriage as such can and should be dispensed with as a separate legal and analytic category. See:Fineman, M. A. 1995. The Neutered Mother, the Sexual Family and Other Twentieth Century Tragedies. New York, London: Routledge.Fineman, M. A. 2001. Why marriage? Virginia Journal of Social Policy and Law 9: 239.Fineman, M. A. 2006. The Meaning of Marriage. In Bernstein, A. (ed.) 2006: 29-69.Bernstein, A. (ed.) 2006. Marriage Proposals: Questioning a Legal Status. NYU Press.

Lots of people collected in Bernstein 2006 follow her lead. Other people I occasionally discuss who take this step include:

See, I wasn't going to go into the whole implication that I don't "really" love my partners. But this? This is the absolute essence. This is requiring that poly people undergo a marriage test (whether that's "sufficient affection" or "sufficient time/attention") that monogamous people don't. People might disapprove of loveless marriages, but they're not illegal. The spouse of a friend of mine spends half the year in Brazil. No-one told them they couldn't get married.

OK, in simplest terms my idea is that marriages with massive amounts of time spent apart (let alone utterly loveless marriages) are highly non-ideal cases. And we all recognize them as such (most such cases wouldn't pass muster as de facto marriage-like relationships for legal purposes). This then tells us that not all of the normative content of the civil marriage institution is something we do, or even could test for.

It's therefore completely compatible with my paper's story that most (or even all) actual mono-marriages are highly non-ideal, and that most (or even all) actual poly arrangements are significantly closer to that (high fulfillment/romantic intimacy) ideal.

Still, even in that outre case, the two sorts of relationships are different structurally/modally. All those empirically failing/low-functioning mono-marriages are structurally fine - each of them could have been ideal had its participants made different choices. The relatively close-to-ideal/high-functioning poly cases, however, weren't ideal and couldn't have been just as matter of their structure (including some comparative static desiderata). Thus there's no discriminatory testing going on in the model I describe only test that I apply to poly cases is the modal test of possibility that applies to all.

I basically say all this in Section 4.2 of Intrins Probs paper, e.g.:

Similarly, marriages that fail to meet normal expectations of personal fulfillment and intimacy are fine, and could even be the statistical norm at least in principle. But certifying as marriages types of relationships that are logically guaranteed to fail to meet such expectations would be a serious mistake. It's perhaps been hard to keep in focus in the long trek through Sections 3.2 and 3.3, and subsequently that all of the temporal details we've discussed are ultimately only relevant for what they tell us about a relationship type's capacity or possibilities, But the latter is in fact our only bottom line. We reject Ms Moderne's candidate PM (after helping her identify what she's proposing) not because some (and in fact all) of its partners actually fail to hit the 100%-partnered mark, but because no relationship with that structure (whose graph is unbalanced bipartite) could have all partners hit that mark.

Here are some further relevant paragraphs from the underlying book:

1. [W]hile various kinds of asymmetrical care-delivery may deserve more legal recognition and state support than they currently get (and a weak, legal super-category that covers them, e.g., Metz 2007's 'intimate care-giving unions', or March 2009a's 'civil unions', might be useful), there's little (if any) reason to doubt that the symmetrical, fully voluntary/consensual, very high-bandwidth partnering up that's civil marriage's traditional focus will continue to be an important personal and social reality that's worthy of special, wider interest. The state and society more generally have strong interests in citizens settling down. Since marriage-like relations are a big part of that for many people, it makes sense for the state to support and help constitute that aspect of settling down by providing standardized legal tools for drawing 'bright lines' of priority and exclusivity (thereby ensuring some measure of orderly, linear process if things fall apart) through otherwise unruly personal and social landscapes (see Part II, esp. Chapters 11, 13, and 14). And if specially recognized and legally articulated marriage-like relations are positive for proliferating relatively robust social building-blocks and growing-points (i.e., that are, on average, net contributors to scarce state resource pools), for providing back-up parents for kids (i.e., if one parent dies), for discouraging multi-partner fertility, and so on, as they appear to be, then so much better. Notwithstanding that the law doesn't 'test' for cohabitation, fertility (see Chapter 3), or any other aspect of either retrospective or prospective connectedness between the parties in question, civil marriage formalizes something that's supposed to be a big deal for the people involved. Marriages are, for this reason, ordinarily taken to be loci for personal challenge and social effort and achievement and assessment. That's a distinctive, rich personal and social attitudinal eco-system that, a priori, appears likely to require its own analytical category. In our view, it's fairly fantastical to suggest otherwise. It's also gratuitously risky (and vaguely Year Zero-ish) to actually try to sink marriage-like relations without trace in much more general pools of personal relations/bonds (regardless of whether those pools are public or private).2. Neither individual nor pairwise infertility/sterility whether it's• congenital• caused by accidents of life and development (e.g., mutilation)• caused by physically necessary features of life and development (e.g., aging), or• by choiceis any legal bar to a contemporary marriage. We could require positive fertility tests as a condition of marriage and/or impose various sorts of simple age and health-related restrictions of the sort that sometimes matter in immigration cases. We could even require fertile couples to swear to try to procreate. But we don't do any of those things. Hence, so the story goes, marriage as we actually legally administer and practise it doesn't have anything essentially to do with reproduction or potential for reproducing. Civil marriage, as it is on the books, not as it is in some traditionalist or Fundamentalist fantasy-land, isn't a procreative institution. Prima facie, if this line of reasoning worked, it would prove too much. For example, romantic and sexual intimacy are part of the ideal of marriage, but we don't 'test' for romantic involvement or sexual intimacy (or anything else much) before issuing marriage licences. Similarly, we don't require people to take a 'compatibility test', let alone to heed its results. Official, public declarations of complete sexlessness with respect to each other (and/or of explicit mutual intentions to pursue sexual relationships outside the marriage) don't disqualify any couples. Neither do explicit announcements of the utter mercenary convenience of the union, of mutual intentions to dissolve the union exactly 1000 days hence, and so on. Concluding on these sorts of grounds that civil marriage has nothing essentially to do with romance, sex, presumptive exclusiveness and permanence, etc. would clearly be premature. To take that route would empty civil marriage of any ideal content whatsoever3. In Chapters 2-5.... we saw no alternative to taking seriously that 'Legally formalized and regulated voluntary love relationship' is the base-line for the whole space of legal/possible marriages. Any procreative core represents a separate, ideal/normal case and its boundary within that broader space of legal/possible marriages. That is our post-Enlightenment background conception of marriage, for better or worse. Someone might try to resist the idea that there is a determinate background conception of marriage of this kind as follows:'Just as we don't require positive fertility tests as a condition of marriage, we don't 'test' for romantic involvement or sexual intimacy (or anything else much) before issuing marriage licenses. We don't require people to take a 'compatibility test', let alone to heed its results. Official, public declarations of complete sexlessness with respect to each other (and/or of explicit mutual intentions to pursue sexual relationships outside the marriage) don't disqualify any couples. Neither do explicit announcements of the utter mercenary convenience of the union, of mutual intentions to dissolve the union exactly 1000 days hence, and so on. Civil marriage has nothing essentially to do with romance, sex, presumptive exclusiveness and permanence, etc.. Indeed, civil marriage has no ideal content whatsoever. Rather, it's a simple act of registration with the state, one that has a range of legal consequences, as it were, downstream. That's it. To suggest that marriage itself is anything more is just fantasy, nostalgia, and the like.'We reject the skeptic's assertion that the normative content of an institution is exhausted by 'what it tests for.' Compare the skeptic's cases of bizarre couples who pre-announce their estrangement from each other and their overall cynicism about what they're doing with announcing that (i) you plan to vote randomly, i.e., without knowing anything at all about the candidates, the parties, their policies, etc., or that (ii) you plan to vote derivatively, say, the way your husband or your priest tells you and contrary to your own well-thought-out views and wishes. There's no mechanism, perhaps no physically possible mechanism to stop you from voting irresponsibly just as there's no mechanism, perhaps no physically possible mechanism to stop you from marrying irresponsibly. But it would be a huge mistake to take that lack of a mechanism (or possible mechanism) to imply that there's no such thing as responsible or irresponsible voting or marrying, or to require us to disavow normative judgments such as 'You shouldn't vote if you can't do so responsibly' and 'You shouldn't marry if you can't do that responsibly either'. Rather, contra the skeptic, we should conclude that marriage and voting alike are normatively rich institutions and that only some of their normative content is legalized or could ever be legalized.

Hope all of that helps. My views may well be wrong, but they're a serious effort to think through the area systematically (with all the details worked though, and limitations noted) and carefully, giving fair hearings to as many objections as possible.

Yes, in this context. Note that I'm not dismissing Fineman by calling her a 'radical'. Fineman is the equivalent in family law of academics in debates over citizenship etc, (another topic I've written on) who want completely open borders, to reduce all notions of citizenship to residency, and so on, e.g., Bauböck, Carens, Bozniak. I don't dismiss any of these people either, but their proposals are very substantial/radical/utopian departures from how the world actually works, so the 'radical' label fits them too.

As far as the Glaister piece goes, say what now? Glaister's excuse for subjecting poly-marriage to greater tests than mono-marriage is that mono-marriage has a chance to succeed but poly-marriage just doesn't.

It's the same test for everyone, see my response to Emma above. No excuses given or needed.

This excuse is erroneous on its own, but also wrong because his arguments as to why poly-marriage doesn't have a chance don't wash. Quite apart from the assumption that a poly relationship would have only a single member of one gender

I don't assume that (and all my technical results apply to graphs with arbitrary nodes). I always start from v-shaped cases but that's not where I end up.

it also continues mono-assumptions about intimacy and relationships -i.e. the "dance-card" analogy, which carries the implicit assumption that you can only dance with one person at once; that intimacy can only occur or be fulfilling on a one-to-one basis. My extremely limited experience and/or observation (no, not intimate observation) of poly relationships and/or intimacy doesn't suggest either of these to be the case; and that at least some poly people might argue for the right to marry on the basis that for them, one-to-one intimacy is less emotionally fulfilling.

Some of this I agree looks bad - there's a constant worry that my main argument might be begging the question against poly folk. But I do spend a lot of time trying to address such points...

Glaister glosses over this possiblity by stating that "there are reasons to doubt that many [cases of 'shared time'] exist", and glosses over what cases there may be as divisible into shorter periods of one-to-one time. At this point, if it wasn't before, I think it's pretty clear that he probably just doesn't understand poly relationships, so there doesn't seem much point in reading any further.

Well people are very good at kidding themselves too (occasionally you'll meet a person with lots of kids or multiple jobs who'll just deny that there's any division of scarce resources going on). I think it's reasonable to look at interpersonal matters in terms of fixed flows of resources (hence to require that whatever the messy reality is must be representable by a graph with a decimal edge-labeling that's itself representable as a mixture of one-factors). Poly folk can flatly deny that any such model applies to them... I try to answer that kind of self-serving denial in various ways, but there may be limits to what can be done. A fallback position for me is therefore to go completely conditional: if poly folk aren't magical critters free of all resources constraints then no PM regulatory regime exists that ensures potential meaningfulness and either respects divorce norms or allows any significant amount of solidity to be expressed.

In general, I'd like to add that the sort of argument I've tried to make very precisely is the sort of argument a lot have people have often wanted: an argument that says exactly why allowing SSM is a conservative extension of our existing marriage regime, and why allowing PM is not (allowing de facto marriage a la NZ isn't either but that's another story). I officially disavow most slippery slope reasoning (at least in the sense that I think such lines of reasoning bite everyone equally), but it's definitely nice to have a definitive answer to the SSM->PM slope (I was pleasantly surprised to discover it). It's disappointing that absolutely nobody thinks that my argt might be of some use.

Instead of - bear with me, this is a bit of a leap - examining people's actual experiences of poly relationships, historical and current? I feel that sociology has just a wee bit more to offer here than mathematics.

Math has its place. Granted some very basic assumptions (which you and many others aren't prepared to grant me) that fulfillment/intimacy work like time/attention/focus, math then tells us what sorts of networks with those links can in principle look and function like. Nothing's being reduced to mathematics, but everything intelligible in the vicinity has to be consistent with it. [Somewhat similarly, there are mathematical differences between OS and SS simply because two-sided and one-sided marketplaces work very differently. SS PM is much less ban-worthy for this reason! See discussion and refers in fn 42 of my Ratios paper.]

Granted some very basic assumptions (which you and many others aren’t prepared to grant me) that fulfillment/intimacy work like time/attention/focus,

I think it is incumbent upon you to demonstrate why those assumptions are valid. That demonstration would need to demonstrate some engagement with psychology, sociology and anthropology that's at least as rigorous as your engagement with graph theory. It could also involve some empirical, qualitative research with poly people about what fulfillment and intimacy mean to them ... if you hadn't already dismissed their experience with "people are very good at kidding themselves".

"I think it’s reasonable to look at interpersonal matters in terms of fixed flows of resources": I think we have very different definitions of the word "reasonable", and that you are so busy applying a strictly abstract ideal of pure reason that you ignore the common English interpretation of "reasonable", and dismiss the idea that le cœur a ses raisons, que la raison ne connaît point. Pure rationalism has its place, but before reducing all interpersonal relations to "resources", it might do to apply some empirical observation of those relations.

It's hard to tell what or who you're quoting at times, and in what context, but I found it intriguing when you said that it is "gratuitously risky (and vaguely Year Zero-ish) to actually try to sink marriage-like relations without trace in much more general pools of personal relations/bonds". This sounds remarkably close to the conservative argument against SSM that it "cheapens" traditional marriages. Are you saying that all these deluded polyamorous sluts are planning to sink real "marriage-like relations" with their promiscuous unfulfilling Ms Moderne arrangements?

Your prioritisation of Rationalist mathematical ideals over the needs and choices of slutty polyamorists is putting Descartes before the whores.

Granted some very basic assumptions (which you and many others aren't prepared to grant me) that fulfillment/intimacy work like time/attention/focus

A/ These are not so much "basic assumptions" as the foundations of all your work, without which it's basically meaningless. Whether they're true, therefore, is far more important than whether the maths is correct.

B/ They're clearly not true. That's why people aren't granting you them. Perhaps the clearest example of this is that if time/attention/focus = fulfillment/intimacy, then for any stay-at-home parent, their most fulfilling and intimate relationship would be with their child. (As long as they only had one child. That relationships would immediately lose significance in a group setting, of course.) And it's about here that you begin to see that the content of the time spent might have something to do with how fulfilling and intimate the relationship is. That perhaps two hours with someone who can make that Descartes joke is worth about ten hours with someone who calls everything "Ba!". And when you start looking at content, at quality rather than quantity, assigning a quantative value to a relationship starts to look... about like it should.

Thanks for your detailed reply Tom. I've kind of saved your reply for last so that I can use other replies I've given as a shorthand. Anyhow....

I think the whole argument is fundamentally flawed by your basic assumptions. It starts with a "background conception of what marriage is - preeminently that it's a voluntary love relationship with high degrees of personal fulfillment and intimacy as its normal aspiration". That's not a definition of marriage, it's a definition of love. "Marriage" is a legal construct that extends a range of rights and responsibilities to (a subset of) people who enter into such voluntary love relationship (VLRs), should they so choose. While you rightly say that in all but fraudulent cases (such as marriages purely for immigration or student loan purposes), people who get married have a VLR, not everyone in a VLR chooses the rights and responsibilities of marriage (presuming they are allowed), for instance because they're not interested in sharing property or having children. Also, your definition includes brief but intense flings as well as platonic friendships and familial relationships.

I think I've said most of what I want to say in reply to this in my reply to Emma. But let's continue and see where this goes.

So, the rest of the article constitutes not of an argument against poly marriage per se, but against the possibility that VLRs can deliver "high degrees of personal fulfillment and intimacy". You consider this a prerequisite for a "marriage-like" relationship, and that thus relationships structurally incapable of delivering this fulfillment should not be given the legal status of marriage - a highly debatable point in itself, but one I won't go into. The core of your graph-theoretical analysis aims to show that any relationship where n>2 cannot deliver the "high degrees of personal fulfillment and intimacy" that can occur when n=2.

I'd add various qualifications, e.g., I end up going 'up a level' to bring in what an overall Poly Marriage tolerant regime that includes divorces would look like. But let that pass.

The vital assumption behind this is in 3.1, where you write "their normal expectations for fulfillment and intimacy, analyzed in the first instance just in terms of time elapsed ... are guaranteed to go unmet". As far as I could see, all of your analysis uses time elapsed as a proxy for fulfillment and intimacy, and there seems to be no "second instance" where you seriously examine any other dimensions.,

In sec 4.4.2 I say:We've repeatedly emphasized that the '1' in this basic (A<--1-->B) case should not be thought of as an actual residency/time value, but rather as a possibility or capacity for spending such time. Behind that, however, as we emphasized in Section 4.1.3, the '1' in this basic case is coding for whatever getting 100% of someone really amounts to in choices such as:(1) She'd rather have 25% of Mr Fabulous than 100% of Joe Schmoe.Time possibly spent is an intelligible proxy for such percentages, but that proxy has limits. Ultimately, even 'possible time' is only a symptom of the underlying normative reality. That reality includes such hard-to-think-straight-about items as:• Entitlements to be attended to• Obligations to care for and stand behindand so on. The sort of locus of fulfillment and intimacy that the '1' codes for in the basic case is a normatively structured event: if you're B then you're supposed to come running when A calls (or have a very good story to tell about why you can't). And because everything's symmetrical, you're entitled to call on A in the same way. Now the obvious point: the '1' in the basic case is supposed to be compatible with having jobs, having time to oneself, and so on. The '1' just means you can be called upon at any time: you can be bothered at work, woken from deep sleep, and so on. Your precious alone-time gets to be interrupted by your partner's latest crisis. And you get to do the same to them. The force of the 'holes' in Table 10 – the thing that makes them deficits and rightly characterizable as episodes of partnerlessness – is that in that case there's no one to come running, no one whose 'job' it is to come running. The obligations and entitlements that are always in force in the basic case (which is not to say that those obligations will be met) are passed around in multi-partner cases, and where there's a 'hole' there's no one left to hold the baby.

Well, I try!

And equating fulfillment and intimacy with time spent is just utterly, stonkingly, face-palmingly wrong. There's a strong correlation in most cases, but it's so far from a clean linear relationship that the clean algebra of your argument becomes useless. And that's even assuming that intimacy can be quantified, which I doubt.

The idea is that if something can't be explained/ratified in those terms then that's an alarm bell. Remember to that this is the ideal case. Particular instances are much more ragged, even if one tries (as I've occasionally tried to do but found it more trouble than it's worth) to cash things out strictly in terms of obligations.

Another flaw is the underlying assumption of equivalence; the idea of "normal expectations". Whose normal expectations? Yours? Everyone has different expectations of the quantity and (vitally important) the qualities of their interactions with their intimate partners. All of your calculations and decimal labeling ignore this.

Again, see my answer to Emma above. But , honestly, a certain amount of vagueness notwithstanding I don't think it's any more of a problem to say what marriages are supposed to be like than it is to say what an ideal voter is.EXAMPLE: (Voters - ideal and non-ideal)Voters in national elections are supposed to know basic facts about:• How their electoral system works• Candidates, parties, and their policies• Important issues confronting the nation• National and world history• Central ideas in politics, economics, and lawDistressingly few people are ideal voters in this sense. But, of course, the average non-ideal voter in this sense is in much better shape than the average barely literate or mostly senile or fairly deranged person, almost all of whom will get to vote in any society that values universal, equal suffrage. That is, there's a workable if rough Voters-With-Knowledge Ideal or VWKI, and there are different tiers of non-ideal voter, all of which nonetheless rightly fall on the 'entitled to vote' side of the votes|doesn't-get-to-vote boundary.

Marriage works the same way. The institution is freighted with expectations that aren't written down anywhere any more than they are in the voting case. Those backgrounds norms do, however, strongly come into play when we're thinking about whether to expand franchises.

Despite the veneer of mathematical rigour, your arguments often come down to personal preferences, prejudice or flat-out denial. You claim that "significant irreducible shared time is impossible" based upon the statement "it's very hard to believe that two or more relationships with the depth of marriages can be conducted substantially, let alone exclusively in parallel time and in a shared space". That's not an argument, it's an admission of your lack of imagination. You follow Nietzsche's comparison of a marriage to a conversation, then state that any conversation with more than two people must have "less depth". Boy, you must be a riot at dinner parties.

It's true, I don't like dinner party's much. I often feel like I've encountered just the intersection of whoever's there, and often that intersection is (understandably) very limited (everyone's got kids, everyone's been to a restaurant recently, ...). But, seriously, I think the kind of shared-resource/flow model I use is the obvious, natural one to try. If nothing like it is true then one wants to see what the model is.

All this would be fine if it were just ethico-mathematical sophistry for the sake of it; a diverting game of arguing about how many angels can get married on the head of a pin. But you seem to be making a serious argument, and suggesting that legal rights should be denied to certain people on this basis, in which case your dismissal of empiricism at the expense of "conceptual" costs and benefits is unforgivable.

I disagree. The concept of marriage in the west evolved away from its original poly-tolerant concept to something pretty determinate and also idealizing (with all sorts of consequences for immigration, legal immunity, and the like). Can that fairly recently purified and symmetrized concept and institution now be expanded to cover arbritrarily complex groups of people if that's what they want? Not without deforming the concept significantly is my answer. (In roughly the same way that having voters who aren't citizens and who can't be representatives deforms the underlying embodied-in-institutions concepts of citizen and democracy.)

If you want to construct a mathematical argument for a legal position, make sure you get your axioms right. And if your axioms are about "personal fulfillment and intimacy" for people who might want a poly marriage, then you can bloody well start by asking some poly people what fulfillment and intimacy mean to them.

As I've indicated before, my project is completely different from ones that focus on the alleged incompatibility of poly arrangements with various aspects of human nature such as jealousy, compatibility etc... That means focusing on slightly idealized models that hold true no matter what if I'm right, so that whatever problems they face can't be self-selected out of. That leads people such as yourself to object to the idealization. Well you would, wouldn't you?

General thought: Probably that's me done. Thanks to everyone for their comments.

This sounds remarkably close to the conservative argument against SSM that it "cheapens" traditional marriages. Are you saying that all these deluded polyamorous sluts are planning to sink real "marriage-like relations" with their promiscuous unfulfilling Ms Moderne arrangements?

No, the kinds of things that Fineman wants to dissolve marriage into are the myriad sort of care-relationships in society, relatives to each other, close friendships, parents-to-kids and the like. Those are what society and the state should be focused on she believes: symmetrical, fully voluntary/consensual, very high-bandwidth relationships linked to sex or love or children, by way of contrast, are from her perspective a kind of ephemeral froth that doesn't even really bear thinking about by the state.

Your point (B) sounds like the sort of thing I have covered pretty well in my Section 4.5.1. Yes, it's the quality/content/high normative bandwidth (mutual obligations and individualistic intelligibility) of adult marriage-like relationships that mean that there's a possibility for an anti-PM argument without inadvertently creating an anti-poly-child argt. But it's been a while since I've thought about this particular move, so I may have to take a raincheck, think things over again, and get back to you on this.

Stephen, I realise you've put a lot of time and thought into this, but I still can't see how maths can give insight into the nature of relationships. Surely it's the people having the relationships who can give us insight? And we should let them tell us how it is?

I've learned a lot from reading Emma's columns and everyone's comments; some of it I find very challenging, but when people talk about their own experience, who am I to say they are wrong or misguided?

I know, at least some of the time, what works for me, but I don't presume to know what works for other people. I'll let them tell me that, if they want to. :-)

I really should stop now: there's so much argument at cross purposes that I doubt we'll get anywhere. In many ways I agree with Fineman that marriage should be deconstructed into a suite of rights and responsibilities that can be chosen to suit the needs of any combination of adults who choose to adopt them. But there's one thing that I can't let go, regardless of the definition of marriage: your argument that because poly relationships divide a finite time resource among more people, they cannot deliver the fulfillment and intimacy (F&I) of a two-person voluntary love relationship (VLR).

a) Even if F&I were strictly proportional to time spent, how much is "enough" to make it equivalent to a two-person situation? I'd suggest that two-person relationships would structurally (if not realistically, given the other requirements of life) offer the potential for far more time together than is needed to generate F&I. Two-person marriage offers a structural overcapacity of potential shared time, so that unless work and family stresses take over, most partners in real-life relationships fill up their F&I tanks after a while, and then go fishing or shopping. Thus, there's potential for the finite time resource to be divided among more people and still give every pair all the time required to give them F&I. Some people take up golf; some take a lover.

b) The argument about obligations and having someone to come running has some weight, but only if you assume that the relationship has to be completely self-contained. I've never known a single relationship that matches that model. In reality, emotional and practical support is offered and shared among much wider networks (family, friends, drinking buddies, Twitter). You don't have to be in a VLR with someone before you come running to their aid: you just have to care about them.

c) Your time calculus also breaks down on this point: while people might be in a VLR with a certain number of people, unless it's a strictly polyfi arrangement it's quite possible that those who are "missing out" (on time, sex, cuddles, support and backgammon) might actually be getting it elsewhere.

d) Throughout, you assume that people who might choose a PM have exactly the same criteria for F&I as everybody else. However, have you considered that for a poly person, a strictly monogamous relationship might never be fulfilling, no matter how much love there is between those people and how much time they get to spend together? Poly folk don't have to be "magical critters free of all resources constraints" to have meaningful relationships with more than one person, and in fact that may be a prerequisite for fulfillment rather than a barrier.

(Admission, I've read the discussion but not Stephen's paper as I don't do pages and pages of maths).

The time issue can only hold any water at all if we think of marriage as an intense, romantic relationship. If we see marriage as a domestic and familial arrangement then it looks very different.

I am (Internet) acquainted with a poly family of four adults and three children and, from what I know, they have a lot of advantages over a two adult family. Double the people engaged in housework and childcare leaves everyone with more time and energy and three full-time incomes allow a rather greater level of comfort than most famiilies with a "stay at home" parent experience. Spreading the domestic and financial burden across more people means that everyone has more, not less, time, energy and resources to spend on their romantic relationships.

I'm afraid Stephen's math leaves me cold...I have enough trouble working out binomial coefficientsbut I'm all for anything that creates a family of positive integers.

Math may be for ever but people can changemaybe there is the odd long division, a little subtractionand even some carrying on but in a universal systemit ain't all fibonacci sequences and phi in the skythere's all kindsa factors involved that can create a polyphase sequence leading to complex roots of unity.Each to their own without doing harm...

However, have you considered that for a poly person, a strictly monogamous relationship might never be fulfilling, no matter how much love there is between those people and how much time they get to spend together?

I suspect, unfortunately, that this might be one of those things that's easier to understand with specifics. So. Huh. My Other Significant Other and I have discussed the impossibility of the two of us ever being able to have a fulfilling monogamous relationship together. We each have needs the other doesn't satisfy, and we both know that, so we'd always know the other was unhappy.

That's one thing that's true. Another is that, from my point of view at least, we have quite simply the fastest and most astonishingly profound intimacy I've ever known in my life.

And I can totally understand people finding it difficult to imagine how these things can co-exist. But I also know that they do.

I don’t think it’s any more of a problem to say what marriages are supposed to be like than it is to say what an ideal voter is.EXAMPLE: (Voters – ideal and non-ideal)Voters in national elections are supposed to know basic facts about:• How their electoral system works• Candidates, parties, and their policies• Important issues confronting the nation• National and world history• Central ideas in politics, economics, and law

Okay, let’s assume that’s a fairly uncontroversial description of the “ideal voter”. That was easy. It should be just as easy for you to describe: “Married persons – ideal and non-ideal” followed by a set of bullet points.

Granted some very basic assumptions (which you and many others aren’t prepared to grant me) that fulfillment/intimacy work like time/attention/focus, math then tells us what sorts of networks with those links can in principle look and function like.

Everyone else has pretty much explained the problems with this, but I'd like to add: if you haven't discovered by now that the application of logic to problems in a constructive way requires premises your target audience can agree with, you're in for a lifetime of disappointment at the rejection of your "definitive answers".

(1) I do find myself wondering who the paper’s intended audience (and their relationship experience) could be.(2) The assumptions made here about evaluating (poly, or any) relationships really are at the level of abstraction of the old joke about physicists (“Assume a spherical cow…”), so it’s not surprising they’re rejected by people with direct experience. (3) I suspect we might find that most humans, and most relationships, by whatever label, and by whatever metric, are

highly non-ideal cases

– but that doesn’t make them meaningless or valueless. The existence of different individuals, different relationships, different meanings, different values, does not entail the applicability of any global scale of “better” or “worse”. Construction of some such scale may be possible, but it is a step that absolutely requires validation from participants.